Deep learning applied to analyze patterns from evaporated droplets of Viscum album extracts

This paper introduces a deep learning based methodology for analyzing the self-assembled, fractal-like structures formed in evaporated droplets. To this end, an extensive image database of such structures of the plant extract Viscum album Quercus \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10^{-3}$$\end{document}10-3 was used, prepared by three different mixing procedures (turbulent, laminar, and diffusion based). The proposed pattern analysis approach is based on two stages: (1) automatic selection of patches that exhibit rich texture along the database; and (2) clustering of patches in accordance with prevalent texture by means of a Dense Convolutional Neural Network. The fractality of the patterns in each cluster is verified through Local Connected Fractal Dimension histograms. Experiments with Gray-Level Co-Occurrence matrices are performed to determine the benefit of the proposed approach in comparison with well established image analysis techniques. For the investigated plant extract, significant differences were found between the production modalities; whereas the patterns obtained by laminar flow showed the highest fractal structure, the patterns obtained by the application of turbulent mixture exhibited the lowest fractality. Our approach is the first to analyze, at the pure image level, the clustering properties of regions of interest within a database of evaporated droplets. This allows a greater description and differentiation of the patterns formed through different mixing procedures.

In Figure S1, the absence of texture information in several sections of the DEM image is noticeable. The loss of resolution in the reduced DEM images is also exhibited in the figure. These represent common problems that appear when considering the analysis of the complete image using convolutional neural networks. For this reason, we turned our attention to texture information provided by image patches.
Original image -size 960 x 720 An overall scheme of the automatic full texture patch selection process is illustrated in Figure S2. The selection begins with the whole DEM image ( Figure S2a), and proceeds with a random patch sampling ( Figure S2b) considering at most thirty percent overlapping area between patches. The idea behind this is to reduce repetitive texture features between patches. The final selection is carried out by means of skewness analysis and PCA-based outliers removal. In Figure S2c, the resulting selected patches for the input image are depicted.

Skewness analysis
Here we provide specifics about the skweness analysis, an important stage of the automatic selection of full texture patches. Once the random patch sampling has been performed, we measure the lopsidedness of the pixel distribution. An example of this for a couple of patches is shown in Figure S3. We compare the mean asymmetry measure of each row and column of the patch in order to detect the absence of texture information. Figure S3 (top) shows a patch that presents a uniform pixel distribution due to the symmetric behavior of its texture information. On the contrary, the patch shown in the bottom row of the figure exhibits absence of texture information, thus asymmetric behavior. The parameters that are evaluated to consider a complete texture patch are the standard deviation for both distributions generated through the mean values of skewness and the slopes of their first-order polynomial fit. Here we provide specifics about the outlier removal process based on PCA, the final stage for the automatic selection of full texture patches. For PCA, each patch is transformed into a column vector t n×1 , where n = 128 × 128 is the number of pixels in the patch. The training set data matrix is constructed by concatenating each vector patch by columns as [t 1 | t 2 | · · · | t k ], where k is the number of patches selected in the analysis of the pixel distribution. The differences from the patch averaget are used to construct the centered training data matrix Principal Component Analysis seeks a set of orthogonal vectors which, in the least square sense, minimize the correlation between the columns of T. The solution is found by calculating the eigenvectors of the covariance matrix Σ Σ Σ n×n = TT T . As Σ Σ Σ is symmetric, there always exist and orthogonal basis U n×n and a diagonal matrix Λ Λ Λ n×n that satisfies the relationship: where U n×n is the eigenvector matrix and the eigenvalues of Σ Σ Σ are the diagonal elements of matrix Λ Λ Λ.

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We observed that the second and third principal components of the patch database were related to texture bias in the patches. Negative outliers for the second principal component presented a bias towards the upper right corner in the patches, while the bias for positive outliers was towards the lower left corner. For the third principal component, negative outliers showed a bias towards the upper left corner, while the bias for positive outliers was towards the lower right corner. These observations are depicted in Figure S4 (left). Finally, to obtain the full texture patch database, we removed the outliers from the second and third eigenvectors. These outliers are depicted with red plus signs in the boxplot of Figure S4 (left). Note that points are considered outliers if they are greater than q 3 + w × (q 3 − q 1 ) or less than q 1 − w × (q 3 − q 1 ), where w is the multiplier whisker, and q 1 and q 3 are the 25th and 75th percentiles of the sample data, respectively. Figure S 6. T mixing procedure image and its spatial location of patches. The image with the highest texture composition in the less fractal category is shown at the top. The twelve patches, which correspond to the less fractal category, are shown at the bottom.

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Patch 1 Patch 2 Patch 3 Patch 9 Patch 8 Patch 7 Patch 4 Patch 5 Patch 6 83 V Figure S 7. L mixing procedure image and its spatial location of patches. The image assigned with the more fractal category is shown at the top. Its nine patches can be observed at the bottom of the figure.